Quantum Synchronizable Codes From Cyclotomic Classes of Order Two over $\mathbb{Z}_{2q}$

TL;DR

This paper introduces two new classes of quantum synchronizable codes derived from cyclotomic classes over _{2q}, which achieve optimal synchronization and exhibit strong error correction for quantum noise.

Contribution

It constructs novel quantum synchronizable codes using cyclotomic classes of order two over _{2q}, reaching the upper bound of synchronization and improving error correction.

Findings

Codes reach the upper bound of synchronization capabilities.

Codes demonstrate good error correction for bit and phase errors.

Construction method based on cyclotomic classes of order two.

Abstract

Quantum synchronizable codes are kinds of quantum error-correcting codes that can not only correct the effects of quantum noise on qubits but also the misalignment in block synchronization. This paper contributes to constructing two classes of quantum synchronizable codes by the cyclotomic classes of order two over $\mathbb{Z}_{2q}$, whose synchronization capabilities can reach the upper bound under certain conditions. Moreover, the quantum synchronizable codes possess good error-correcting capability towards bit errors and phase errors.